NEW YORK, Dec 17 (Reuters) - U.S. stocks paced a decline in global equity markets on Thursday a day after the Federal Reserve's first interest rate hike in nearly a decade, as continued pressure on oil weighed on the energy sector.

The long-anticipated though modest increase in the federal funds rate also boosted the dollar to a fresh two-week high against a basket of major currencies, while Wall Street was on pace to snap a three-day winning streak.

Economic data pointed to continued healing in the labor market, which could prompt more rate hikes from the Fed next year. However, the manufacturing sector continues to struggle, generating some nervousness among investors.

"Given the higher level of volatility and frankly a little bit of disappointment in some of the economic data and corporate profit data this morning, it could just be more of a knee jerk reaction after we've had a very sharp rally," said Jeremy Zirin, head of investment strategy at UBS Wealth Management Americas in New York.

Brent and U.S. crude oil prices fell and remained near multi-year lows on oversupply concerns and strength in the dollar.

The oil woes helped push U.S. equities lower after rallying on Wednesday, with the S&P energy index down 1.8 percent as the worst performing of the 10 major S&P sectors.

"Certainly there is going to be some linkage but the reason that oil has fallen isn't because of the strength of the dollar it is largely because of the huge influx of supply and production growth across the world, particularly in North America," said Zirin.

Stocks in Europe gained, however, as investors there took the Fed hike as a sign of confidence in the world's largest economy.

The Dow Jones industrial average fell 135.66 points, or 0.76 percent, to 17,613.43, the S&P 500 lost 18.32 points, or 0.88 percent, to 2,054.75 and the Nasdaq Composite dropped 32.97 points, or 0.65 percent, to 5,038.16.

MSCI's all-country world index lost 0.4 percent, even as the pan-European FTSEurofirst 300 index jumped 1.3 percent to close at 1,434.48.

The dollar index, which measures the greenback against a basket of other major currencies, was up 1.3 percent at 99.158, on pace for its biggest percentage gain since Oct 22. The euro lost 0.8 percent at $1.0848, illustrating the diverging paths of the Fed and European Central Bank.

Moves in short-term U.S. Treasuries were modest, After touching 1.021 percent on Wednesday, a 5-1/2 year high, yields on two-year notes were last at 0.9966 percent. However, yields on the benchmark 10-year Treasury notes fell to 2.2534 percent, up 10/32 in price as investors turned their attention to timing of the next hike.

Another sustained rise in the dollar could put more pressure commodities, by making them more expensive when measured in other currencies.

Copper lost 1.3 percent and is down nearly 28 percent for the year so far. Spot gold hit a two-week low of $1,047.25 an ounce and was last at $1,050.60.